The sum of the digits of a two-figured number is 9. If the digits are interchanged, the resulting number equals the original number plus the sum of the digits

Question

My number is ???

Answer 1

Here is an algebraic solution:

 

A two digit positive integer can be expressed as 10 times the tens digit plus the ones digit.  For example, 38 = 10(3) + 8.

 

Let x = tens digit of the number

     y = ones digit

 

Then x + y = 9

       10y + x = 10x + y + x + y

 

Simplifying, we have x + y = 9

                           10x = 8y

 

Since x+y = 9, y = 9-x

 

So, 10x = 8(9-x)

 

      10x = 72 - 8x

 

      18x = 72

 

         x = 4 and y = 9-x = 5

 

The number is 45.

 

 

Answer 2

The answer is 45

4+5=9

54=45+9

Answer 3

The original number is 45.

 

Check it by reversing the digits. You get 54.

54 is the original number (45) plus the sum of the digits (9).